Average Error: 52.0 → 52.0
Time: 5.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r80371 = 9.0;
        double r80372 = x;
        double r80373 = 4.0;
        double r80374 = pow(r80372, r80373);
        double r80375 = r80371 * r80374;
        double r80376 = y;
        double r80377 = pow(r80376, r80373);
        double r80378 = r80375 - r80377;
        double r80379 = 2.0;
        double r80380 = r80376 * r80376;
        double r80381 = r80379 * r80380;
        double r80382 = r80378 + r80381;
        return r80382;
}
↓
double f(double x, double y) {
        double r80383 = 9.0;
        double r80384 = x;
        double r80385 = 4.0;
        double r80386 = pow(r80384, r80385);
        double r80387 = r80383 * r80386;
        double r80388 = y;
        double r80389 = pow(r80388, r80385);
        double r80390 = r80387 - r80389;
        double r80391 = 3.0;
        double r80392 = pow(r80390, r80391);
        double r80393 = cbrt(r80392);
        double r80394 = 2.0;
        double r80395 = r80388 * r80388;
        double r80396 = r80394 * r80395;
        double r80397 = r80393 + r80396;
        return r80397;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 52.0

    \[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)}} + 2 \cdot \left(y \cdot y\right)\]

  4. Simplified52.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}} + 2 \cdot \left(y \cdot y\right)\]

  5. Final simplification52.0

    \[\leadsto \sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))